Compact well-bounded operators
Every compact well-bounded operator has a representation as a linear combination of disjoint projections reminiscent of the representation of compact self-adjoint operators. In this note we show that the converse of this result holds, thus characterizing compact well-bounded operators. We also apply this result to study compact well-bounded operators on some special classes of Banach spaces such as hereditarily indecomposable spaces and certain spaces constructed by G. Pisier.
1 Some of this work forms part of the PhD research of the first author undertaken at Murdoch University under the supervision of Ken Harrison.
2 The research of the second author was supported by the Australian Research Council.